This is a very interesting question, and one I'd never really considered before. You don't specify a time period so I'll chime in with what I know about my specific area (later Middle Ages and Renaissance in Italy, or roughly 1300-1600).

My short answer: I'm totally unaware of sources that talk about the actual detritus of marble carving (i.e., pieces too small for use in other sculptures). But I'll expand a bit and offer some thoughts.

First, whenever it was possible, marble was shaped into a form very close to the intended final size at the quarry. The blocks might be sent down the mountain in rough shape but before further transport they would be individually refined and prepared according to the instructions of whoever was ordering the marble (the sculptor or architect or patron/s, etc.). This was to get rid of as much excess marble as possible before shipping. Marble is heavy, and the cost of transport increased with the weight. In Italy, shipping stone from quarries in the area around Carrara to Florence might involve several different legs over land and water and as many as five loadings and off-loadings at ports.

So a stone that was meant to end up as a figure would often be roughed out in a vague anthropomorphic shape; a column capital or other architectural member would have a different shape; and so on. All to save on transport costs. In some instances the sculptor themself might go to the quarry to rough out the block before having it shipped; this is allegedly what Agostino di Duccio did with the enormous block of marble that would eventually become Michelangelo's David (Michelangelo received the commission after Agostino and another sculptor both failed to complete it—or to do much of anything, really).

The result is that stones arriving in sculptors' or stonemasons' studios and workshops probably had far less "excess" material than we tend to imagine. Much of the marble that was carved away would simply be dust (Leonardo da Vinci, who was famously dismissive of marble carving, said sculptors ended up looking like bakers because they were so covered in marble dust at the end of a workday).

I'm guessing here, but I wouldn't be surprised if larger pieces (that were still far too small for reuse) ended up being burned in lime kilns. The need for building materials in the Renaissance (and in Rome especially) meant LOTS of marble—notably from ancient buildings and sculptures—ended up in lime kilns.

A good general intro to marble and quarries can be found in A. Victor Coonin's From Marble to Flesh: The Biography of Michelangelo's David (2014); if you want to follow up on his main English-language sources you can check out William E. Wallace, Michelangelo at San Lorenzo: The Genius as Entrepreneur (1994) and Luciana and Tiziano Mannoni, Marble: The History of a Culture (although this seems harder to find).